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Masja [62]
3 years ago
9

Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100

grams of part thereof. What could be the weight in grams of a package for which the charge is $1.55?

Mathematics
1 answer:
lukranit [14]3 years ago
3 0

Answer:

  1050 g < weight ≤ 1150 g

Step-by-step explanation:

Let w represent the weight of the package in grams. The the number of 100-gram increments after the first 250 grams is given by ...

  ⌈(w-250)/100⌉ . . . . . . . where ⌈ ⌉ signifies the <em>ceiling</em> function

and the charges for a package exceeding 250 grams will be ...

  0.65 + 0.10⌈(w -250)/100⌉ = 1.55

  0.10⌈(w -250)/100⌉ = 0.90 . . . . . . . . subtract 0.65

  ⌈(w -250)/100⌉ = 9 . . . . . . . . . . . . . . . divide by 0.10

  8 < (w-250)/100 ≤ 9 . . . . . . . . . . . . . . meaning of ceiling function

  800 < w -250 ≤ 900 . . . . . . . . . . . . . multiply by 100

  1050 < w ≤ 1150 . . . . . . . . . . . . . . . . . add 250

The weight in grams could be greater than 1050 and at most 1150 for a charge of $1.55.

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The fish population in a certain lake rises and falls according to the formula F = 3000(23 + 11t − t2). Here F is the number of
Gemiola [76]

Answer:

a) On January 1, 2017 the fish population will be the same as the initial population.

b) On September 18th, 2018 the fish population will be zero.

Step-by-step explanation:

Hi there!

a) First, let´s write the function:

F(t) = 3000(23 + 11t − t²)

The population on January 1, 2006 is the population at t = 0. Then:

F(0) = 3000(23 + 11· 0 - 0²)

F(0) = 3000 · 23 = 69000

This will be the population every time at which t² - 11t = 0. Then let´s find the other value of t (besides t = 0) that makes that expression to be zero:

t² - 11t = 0

t(t - 11) = 0

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and

t - 11 = 0

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On January 1, 2017 (2006 + 11), the fish population will be the same as the initial population.

b) We have to obtain the value of t at which F(t) = 0

F(t) = 3000(23 + 11t − t²)

0 = 3000(23 + 11t − t²)

divide both sides of the equation by 3000

0 = 23 + 11t − t²

Let´s solve this quadratic equation using the quadratic formula:

a = -1

b = 11

c = 23

x = [-b ± √(b² - 4ac)] / 2a

x = 12.8  ( the other value of x is negative and therefore discarded).

After 12.8 years all the fish in the lake will have died.

If 1 year is 12 months, 0.8 years will be:

0.8 years · 12 months/year = 9.6 months

If 1 month is 30 days, 0.6 month will be:

0.6 month · 30 days / month = 18 days

All the fish will have died after 12 years, 9 months and 18 days from January 1, 2006. That is, on September 18th, 2018.

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Step-by-step explanation:

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Answer:

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